Butyl rubber or polythene pond liners are easy enough to repair you take care and do the job properly. Finding the leak is probably the most difficult part of the operation.
The easiest way to find a leak with a butyl liner, is simply let the water find its leaking level. This will be where the cut or hole will be. However, once you have got the water level to the leak, it may still be difficult to see the actual problem area unless it is a big hole or tear.
So, take out a further few inches of water either by siphoning or with your eclectic pond pump. If this is done on a sunny day, the liner will soon dry - except for the area where the leak is! Water will be finding its way back through the liner from the sodden soil behind. So, now you have found your leak, this is what you do!
Get along to your aquatics shop and buy the correct patching material for your particular liner. Either Butyl repair patches or for plastic.